Title

Presenting Functors on Many-Sorted Varieties and Applications

Document Type

Article

Publication Date

2010

Abstract

This paper studies several applications of the notion of a presentation of a functor by operations and equations. We show that the technically straightforward generalisation of this notion from the one-sorted to the many-sorted case has several interesting consequences. First, it can be applied to give equational logic for the binding algebras modelling abstract syntax. Second, it provides a categorical approach to algebraic semantics of first-order logic. Third, this notion links the uniform treatment of logics for coalgebras of an arbitrary type T with concrete syntax and proof systems. Analysing the many-sorted case is essential for modular completeness proofs of coalgebraic logics.

Comments

This article was originally published in Information and Computation, volume 208, issue 12, in 2010. DOI: 10.1016/j.ic.2009.11.007

Copyright

Elsevier

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